Although PC is not known as a climbing area per se, there are a couple area crags worth traveling/hiking to. The Quarry Mountain Crag has good selection of moderate sandstone climbing and bouldering without having to travel to Moab. Located on the southern slope of Quarry Mountain above the Mcleod Creek trail. Prior mention listed as Park City boulder garden, the area highlighted here shows the larger area adjacent with a more fitting name.
Travel into Park City via State road 224. When passing Canyons start to look left for what looks like an old quarry. Head East on 224, look for the Mcleod Creek parking area on the left. Park and back track (westerly) along the McLeod Creek trail. Look up and right for the old mine quarry poles. Much of the climbs exist 20 yards up the hill.